Electrodynamics with Lorentz-violating operators of arbitrary dimension (0905.0031v2)

Abstract: The behavior of photons in the presence of Lorentz and CPT violation is studied. Allowing for operators of arbitrary mass dimension, we classify all gauge-invariant Lorentz- and CPT-violating terms in the quadratic Lagrange density associated with the effective photon propagator. The covariant dispersion relation is obtained, and conditions for birefringence are discussed. We provide a complete characterization of the coefficients for Lorentz violation for all mass dimensions via a decomposition using spin-weighted spherical harmonics. The resulting nine independent sets of spherical coefficients control birefringence, dispersion, and anisotropy. We discuss the restriction of the general theory to various special models, including among others the minimal Standard-Model Extension, the isotropic limit, the case of vacuum propagation, the nonbirefringent limit, and the vacuum-orthogonal model. The transformation of the spherical coefficients for Lorentz violation between the laboratory frame and the standard Sun-centered frame is provided. We apply the results to various astrophysical observations and laboratory experiments. Astrophysical searches of relevance include studies of birefringence and of dispersion. We use polarimetric and dispersive data from gamma-ray bursts to set constraints on coefficients for Lorentz violation involving operators of dimensions four through nine, and we describe the mixing of polarizations induced by Lorentz and CPT violation in the cosmic-microwave background. Laboratory searches of interest include cavity experiments. We present the theory for searches with cavities, derive the experiment-dependent factors for coefficients in the vacuum-orthogonal model, and predict the corresponding frequency shift for a circular-cylindrical cavity.

• The paper presents a comprehensive classification of gauge-invariant Lorentz- and CPT-violating operators using spin-weighted spherical harmonics.
• It derives a general covariant dispersion relation that predicts photon birefringence, dispersion, and anisotropy effects.
• Implications include constraints from astrophysical observations and laboratory experiments that enhance searches for Lorentz invariance deviations.

Electrodynamics with Lorentz-Violating Operators of Arbitrary Dimension: An Examination of Theoretical Extensions

The paper "Electrodynamics with Lorentz-violating operators of arbitrary dimension" by V. Alan Kostelecký and Matthew Mewes explores an in-depth theoretical analysis of electrodynamics incorporating Lorentz and CPT violation, utilizing operators of various mass dimensions. This approach extends the Standard-Model Extension (SME), taking into account the potential for minuscule deviations from Lorentz invariance that may be predicted by overarching physical theories, such as those involving quantum gravity.

Theoretical Framework

The authors classify all gauge-invariant Lorentz- and CPT-violating terms using a decomposition into spin-weighted spherical harmonics, showing that the resulting Lorentz-violating effects in the photon propagator are dictated by nine independent sets of coefficients. These coefficients are characterized by their contributions to birefringence, dispersion, and anisotropy.

1. CPT-odd Operators: These affect photon propagation through altering both phase velocities and polarization modes, yielding birefringence.
2. CPT-even Operators: Categorized further by their contribution to birefringence and non-birefringent effects; they can also lead to dispersion effects that are observable under specific circumstances.

Implications for Photon Propagation

One of the fundamental outcomes highlighted in the article is the derivation of a general covariant dispersion relation, which can be used to predict modifications in photon behavior due to Lorentz-violating effects. The work demonstrates that for CPT-even coefficients, a Weyl decomposition of the constitutive tensor effectively separates non-birefringent effects (attributed to an effective metric distortion) from birefringent effects (related to the Weyl part).

Practical and Theoretical Implications

This research has several implications:

• Astrophysical Observations: By applying the theoretical model to observational data, such as from gamma-ray bursts, constraints can be established on the coefficients governing Lorentz violation. Such studies may exploit outcomes on birefringence and dispersion for light over cosmological distances.
• Laboratory Experiments: The processed framework allows for the exploration of Lorentz-violating coefficients in terrestrial settings, such as cavity resonance experiments. These can potentially probe different coefficient dimensions that are not accessible via astrophysical observations, particularly those affecting non-birefringent behaviors.

Future Developments in Theory and Experiment

The paper suggests potential avenues of exploration, including the possibility of novel experimental setups that could detect non-vacuum birefringence and dispersive effects, providing further insights into Lorentz symmetry breaking at attainable energy levels.

Conclusion

The authors offer a comprehensive theoretical structure that advances our understanding of Lorentz and CPT violation in electrodynamics. This work has broad implications not only for fundamental physics but also for practical tests of the Standard-Model Extension, potentially driving forward the exploration of new physics at the intersection of quantum mechanics and relativity. Overall, this research places a compelling emphasis on the need for synergistic approaches combining astrophysical and laboratory data to discern the subtle marks of Lorentz violation across possible scales.